Question

In the figure, BC = 10 cm, AC = 6 cm and the area of ∆ ABC
is 15 sq cm. Find:
(a) the value of h
(b) the value of k.​

Answer 1

In ∆ABC,

A(∆ABC)= 15sq.cm,

Side BC is a base of the triangle and h is a height of a triangle.

BC=10cm, AC=6cm

A(∆ABC)= 1/2 base × height

15 = 1/2 × BC × h

15 = 1/2 × 10 × h

15 = 5 × h

h = 15/5

h = 3cm

In ∆DBC, angle BDC = 90°

BC=10cm, DC=6cm and BD=k

By Pythagoras theorem,

Hypt²= side² + side²

BC²= BD² + DC²

10²= k² + 6²

100 = k² + 36

100 - 36 = k²

k² = 64

taking squareroot,

k = 8cm